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What the hell is a wave function?
I understand the basics of functional analysis and C* algebras, operators on Hilbert spaces, the correspondence between classical statistical mechanics (probability measures as the extreme points of the dual space to C(X), where X is supposed to be the R^n space representing position and momentum), but what are the wave functions?
Are they actual L^2 functions? Are we talking about L^2(R^3) or something like that, so that the wave functions are literally functions that can be evaluated?